Translator for HPLC HINTS and TIPS for Chromatographers

Saturday, June 27, 2015

K Prime (also known as: Capacity Factor, Ratio or Retention Factor): One of the Single Most Important HPLC Parameters of All

The role of Capacity Factor / Ratio (K prime) in chromatography is to provide a calculation or formula which defines how much interaction the solute (sample peak) has with the stationary phase material (the relative time interacting with the support vs. the mobile phase). If this interaction is too short, then no chromatography has taken place and you have just developed a "flow-injection" method (no column used) instead of a chromatography method. It must be long enough to demonstrate that the method developed is specific to the sample and shows good selectivity for the sample analyzed.

Observance of the fundamentals of chromatography are key to developing high quality HPLC methods. For most modes of HPLC separation, highest on this list of fundamentals is that the sample(s) be retained on the HPLC column used and not eluted out at or near the column void volume (we often refer to this time in minutes as, "T-zero"). Sounds rather obvious at first, but you may be surprised to learn that many chromatography methods fail this test of retention and are invalid. Knowing a sample's retention or capacity factor allows us to be confident that it has eluted past this critical point, but to calculate it we first need to know the column's void volume. Calculation and/or measurement of the Column Void Volume should be one of the very first chromatography method development tasks you learn to perform. Knowing the column void volume allows you to determine the retention time of an unretained sample and the resulting retention factor (K prime) of each sample eluted after it. To do this, you must calculate the column void volume AND inject a sample which will not be retained by the column to determine what time an unretained sample will be eluted off the column. This establishes what we often refer to as the 'T' zero time, or T(0). The time it takes an unretained compound to elute off the column is critical to know. If your HPLC method does not retain the sample on the column long enough past this time, then you are not allowing any chromatography to occur. Once you have this T(0) value, you can then determine the retention factor (the "K Prime") of your actual sample(s) using the simple formula below. Your final method should baseline separate all compounds apart and, if properly developed, each sample peak will often have K Prime values between 2.0 and 10.0. Try and insure that the earliest eluting peak has a K Prime of  >1.5 and do not develop methods which only result in K Primes of less than 1.5 (poor quality chromatography). 

Note 1: Many regulatory agencies (e.g. FDA) require that K prime values be equal or greater than 2.0 to meet Specificity acceptance criteria. After all, if it elutes at or near the void volume, then your method is not specific for anything. Besides being unscientific in design, your method will fail validation if it does not meet this basic requirement.

  • K Prime (Capacity Factor or Retention Factor) Formula:
  •  k1 = T(R) - T(0) / T(0)
    (where T(R) equals the retention time of the peak in minutes and T(0) is
    the retention time of an unretained peak). 
  • *The 'K Prime' of your sample must be > 1.00. A value greater than 1.5 should be your goal.
Example #1: 
 T(0) found to be 2.90 minutes and the sample elutes at 5.80 minutes. k1 = 5.80 - 2.90 / 2.90. k1 = 1.00.

Example #2:
 T(0) found to be 2.90 minutes and the sample elutes at 9.10 minutes. k1 = 9.10 - 2.90 / 2.90. k1 = 2.13.

Example #3:
 T(0) found to be 1.75 minutes and the sample elutes at 1.74 minutes. k1 = 0. No retention and no chromatography have taken place at all. The method is invalid.

Note 2: I see and read published HPLC methods (including "Validated Methods" !) every week which ignore this fundamental requirement and present data showing little to no retention of the primary sample on the column. Most are RP methods run on popular C18 columns and show the main peak of interest eluting out as a nice sharp peak right at the void volume.  These methods often describe the sample analyzed as "100% pure" and are fully validated (because the person doing the work did not in fact have any HPLC experience or training)! A mixture will always look like a single peak by HPLC when no 'chromatography' is employed to separate out all of the possible components. The sample must be retained on the column for a period of time before we can conclude anything about its purity by the method employed.

Note 3: In some cases, when other modes of chromatography are utilized (e.g. size exclusion chromatography; GPC), K prime is not as relevant. This is because size exclusion chromatography relies on the sample's interaction with well defined pores inside the support (inclusion/exclusion) to separate based on molar size. A variety of pore sizes can be used to "filter" the sample. So a large K prime value might be normal for a molecule that is low in molecular weight and spends a lot of time working its way through the column. A high molecular weight sample might just "shoot" through the column due to little or no interaction with the pores. You still need to have retention on the column, but now it is determined by how long it takes the sample to find its way out of the column. This article is presenting for the far more common cases where traditional NP or RP methods are used. In these cases, low K prime values indicate no retention took place and the method fails all claims of specificity for the sample (selectivity is poor).